CMSA Geometry and Mathematical Physics Seminar: Why do Feynman integrals know Calabi-Yau geometry?

Feynman integrals provide a rich source of Calabi-Yau geometry, but the geometric origin of these structures is often obscure. I will describe a simple point of view that begins with two-dimensional examples and leads naturally to moduli problems for vectors and polyhedra in three dimensions. I will discuss recent results for tetrahedral moduli and some new phenomena for pentahedral geometry that point toward a broader geometric framework for the Calabi-Yau structures appearing in Feynman integrals.